Rotating UV with precision
With the part of the UV map selected that you want to rotate, hit R to enter rotation mode, then type the number of degrees with the numpad, for example 90 to rotate it 90°. Then hit Enter or Return to apply it, or just left click.

You can also scale the selection with S and then entering a numerical value, for example 2 to make it twice as large, or .5 to make it half the size.

You can also move the selection along the X or Y axis by hitting G to grab it, then constraining it to the X or Y axis with X or Y, then entering the number of units you want it to move.

This also works in the 3D viewport. If you look at the bottom of the current viewport while doing a resize, scale, or movement operation, you can see the values you have entered in the bar beneath the viewport.